Integration Sum Help

Evaluate

$\Large{\sum _{ n=1,3,5,7.... }^{ \infty }{ \frac { { e }^{ \left( 2n-1 \right) } }{ \int _{ 0 }^{ n+1 }{ \frac { { x }^{ e }{ e }^{ x } }{ \left( x+1 \right) ! } dx } } } }$

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

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@Tanishq Varshney,@Otto Bretscher,@Brian Charlesworth,@Michael Mendrin,@Aditya Kumar

Department 8 - 4 years ago

@Jake Lai

Department 8 - 4 years ago

Very unlikely this series has a closed form. Factorials/gamma functions in integrals, especially in denominators of integrals, are difficult to evaluate in general.

It is best to proceed in the direction of a motivating problem which applies integration in its solution, or to build a problem on the back of techniques already well-studied.

Jake Lai - 4 years ago

@Jake Lai – I made it accidently

Department 8 - 4 years ago

@Pi Han Goh

Department 8 - 4 years ago

What have you tried? What makes you think there's a closed form?

Pi Han Goh - 4 years ago

I don't know I just made this problem and asked my school teacher, she said it was pretty tough. So I asked for help.

Department 8 - 4 years ago

Not all series /integrals has a nice closed form.

Pi Han Goh - 4 years ago

I'm currently busy now. Ty using the infinite product of gamma(x+2)

Aditya Kumar - 4 years ago

@Jonas Katona

Department 8 - 4 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$